An EOQ model for perishable product with special sale and shortage

In this paper, for the first time, an inventory control model to determine the optimal order and shortage quantities of a perishable item when the supplier offers a special sale is developed. Four possible cases based on decision that the purchaser might make about the first replenishment policy (using regular economic order quantity model at reduced price or regular price), if he did not take the special order, and coincidence of special period length with positive or negative inventory level of the last regular period length during the special period, are investigated. Moreover several useful theorems are suggested through which one can find closed-form solution directly when there are integer operators involved in an objective function. At the end, in order to illustrate the proposed theorems and the solution method some numerical examples are solved and a sensitivity analysis is reported too.